SUPERGEN Wind Wind Energy Technology Session 5 Wind Turbine Scaling and Control W. E. Leithead Supergen 2 nd Training Seminar 24 th /25 th March 2011
Wind Turbine Scaling and Control Outline Introduction How big will wind turbines be? Central controller and size Load imbalance reduction Conclusion 2
Introduction??? 2005 1980 1985 1990 1995 2000 3
Introduction Over the last 20 years there has been an almost exponential growth in the size of wind turbines. In offshore machines, the trend is towards bigger machines with taller towers. Does this trend have any consequences for the controller and visa versa. 4
Introduction Conventional scenario Variable speed pitch regulated wind turbine Above rated operation Pitch control of rotor/generator speed 5
Torque (Nm) Introduction x 10 6 3 11 m/s 2.5 96% 97% 10 m /s 98% 2 9 m /s 99% 8.85 m/s 1.5 8 m /s 1 6 m /s 7 m /s 1013456.1817 2 99% 98% 97% 96% 0.5 Beginning 5 of m Stall /s 4.64 m/s 4 m /s 0 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Rotor Speed (rad/s) Typical operating strategy 6
How big will wind turbines be? Drivers for Up-scaling Utilities like power in multi-megawatt scale units. In a wind farm, a number of infrastructure items reduce in cost per MW of installed capacity, the larger the capacity of the wind turbine units. Larger turbines can often use land and wind more effectively. In public funding of wind energy, size has tended to be regarded as a metric of technology progress. 7
max take off weight [t] How big will wind turbines be? Growth in the aircraft industry 1000 100 10 1 1930 1940 1950 1960 1970 1980 1990 2000 2010 year 8
nameplate rating [kw] How big will wind turbines be? 10000 Growth in the wind industry System re-design from 1000 blade to grid connection Low cost 100 Low maintenance Ultra high reliability Full-scale 10demonstrator 1975 1980 1985 1990 1995 2000 2005 2010 year 9
How big will wind turbines be? Is there a limit to size? What influences it? Basic scaling laws rated power scales as square of length scale strength scales as square of length scale mass scales as cube of length scale inertia scales as fifth power of length scale Materials limit ultimate structural feasibility Are these scaling laws seen in wind turbines? 10
mass of 3 blades, M [t] How big will wind turbines be? 60 50 40 30 Blade Mass Scaling RE power 5MW M = 0.0046D 1.923 Siemens 3.6MW Multibrid M5000 Enercon E-112 20 10 0 40 60 80 100 120 140 diameter D [m] Improvement in technology disguises true scaling 11
shaft mass [kg] How big will wind turbines be? Shaft Mass Scaling 35000 30000 25000 20000 15000 10000 5000 M s = 0.01698D 3 0 0 50 100 150 rotor diameter [m] 12
normalised mass [kg] How big will wind turbines be? Hub mass scaling 35000 30000 25000 20000 15000 10000 5000 0 M hub = 0.0057x 3.45 0 20 40 60 80 100 diameter [m] 13
tower mass, Mt [kg] normalised tower mass, Mtn [t] How big will wind turbines be? Tower mass Normalised tower mass 400 400 300 300 200 200 100 Mt = 0.0227D 2.0135 R 2 = 0.6865 0 40 50 60 70 80 90 100 110 120 diameter, D [m] 100 Mtn = 0.0015D 2.6314 R 2 = 0.9434 0 40 50 60 70 80 90 100 110 120 diameter, D [m] 14
How big will wind turbines be? Adverse scaling effects are evident but not as bad as expected This is due to technology advance To see full effect would need today s technology to be applied to smaller turbines Are these adverse scaling effects affecting the price of wind turbines? 15
specific cost [$/kw] How big will wind turbines be? Scaling of turbine price/kw 2000 1500 land based designs offshore, higher tip speed designs 1000 500 0 0 20 40 60 80 100 diameter [m] 16
specific cost, C [ /kw] How big will wind turbines be? Scaling of turbine price/kw 1400 1200 1000 800 600 400 C = 6.6667D + 498.32 200 0 40 50 60 70 80 90 diameter, D [m] 17
How big will wind turbines be? Minimum cost of turbine has been reached. Minimum cost of energy occurs at bigger size due to balance of plant costs installation operation and maintenance grid connection For onshore wind turbines, the minimum cost of energy is achieved with turbines between 3MW and 3.5MW For offshore wind turbines, the minimum cost of energy is achieved with turbines between 9MW and 10MW 18
Central controller and size V T A Aerodynamics Drivetrain R T G g b Actuator b d Controller V Wind speed R g Rotor speed Generator speed T A T G b d b Aerodynamic torque Generator torque demand Demanded pitch angle Blade pitch angle 19
Central controller and size Above rated speed control loop Assume T G constant Simple model Controller Actuator b Drive-train R Drive-train dynamics are influenced by structural dynamics 2 modes for the tower 2 modes for the blades 20
Central controller and size Dynamics from pitch demand to generator speed. blade flap frequency tower frequency blade edge frequency 21
Central controller and size The models have been validated against both measured data and aero-elastic simulations 22
Digression: Linear control basics Transfer functions Transfer functions model the dynamics b s b s... b s bm Gs ; m n a s a s a s a m m1 0 1 m1 n n1 0 1... n1 Roots of the denominator are the poles. Unstable poles have negative real parts. Roots of the numerator are the zeros. Non-minimum phase zeros have negative real parts. n Gs () 1 s 1 unstable Gs () ( s 1) 2 2s 3s1 non-minimum phase 23
phase [deg] magnitude [db] Digression: Linear control basics Dynamics represented by transfer function G(s) Gs () 1 s=jω G( j) 1 s 1 j 1 Horizontal axis: log 10 (frequency in rad/s) Vertical axis (top): 20log 10 ( G(jω) ) Vertical axis (bottom): Arg(G(jω)) 0-20 -40 10-2 10-1 10 0 10 1 10 2 0-50 -100 10-2 10-1 10 0 10 1 10 2 frequency [rad/s] gain phase 24
Phase (deg) Magnitude (db) Digression: Linear control basics Stability margins Phase and gain margins positive closed loop stable 10 5 0-5 -10-15 -20 360 270 Bode Diagram Bode plot for open-loop Gain Margin Phase Margin 180 90 10-2 10-1 10 0 10 1 Frequency (rad/sec) 25
Digression: Linear control basics Design trade-off Maximum phase loss possible is 180 degrees Improvements to all aspects of performance costs phase Zero sum game 26
Digression: Linear control basics Delay Delay of t seconds has transfer function G() s s e t s=jω G( j) j e t Gain = 1 Phase = -t Does nothing other than lose phase Performance inevitably lost 27
Amplitude Gs () ( s 1) 2 (2s 3s1) Digression: Linear control basics ( s 1) ( s 1) (1 s) 2 2 (2s 3s 1) (2s 3s 1) (1 s) Non-minimum phase zero has non-minimum phase zero at 1rad/s and (1 s) e (1 s) 2s Non-minimum phase zero is similar to a delay 1.2 1 0.8 0.6 Step Response 0.4 Again, performance inevitably lost 0.2 0-0.2 0 2 4 6 8 10 12 14 16 18 Time (sec) 28
Phase (deg) Magnitude (db) Digression: Linear control basics 20 Crossover frequency Bode Diagram 10 0-10 -20-30 -40 0 crossove r frequenc y -45-90 -135-180 10-2 10-1 10 0 10 1 Frequency (rad/sec) Performance improves with crossover frequency of open-loop Bode plot 29
Digression: Linear control basics Poles and zeros Crossover frequency is bounded below by any unstable pole Crossover frequency is bounded above by any non-minimum phase zero Unstable poles and non-minimum phase zeros impose absolute bounds on performance 30
Central controller and size Dynamics from pitch demand to generator speed. Non minimum phase zeros Non minimum phase zeros 31
Central controller and size The dynamics from pitch demand to generator speed have pairs of RHPZs First pair is induced by the rotor dynamics Second pair is induced by the tower dynamics 32
Central controller and size RHPZs for a 3MW wind turbine 33
Central controller and size Zeros due to rotor dynamics 34
Central controller and size RHPZs for a 5MW wind turbine 35
Central controller and size Zeros due to rotor dynamics 36
Central controller and size To match wind speed characteristics, crossover frequency needs to be 1rad/s RHPZs limit crossover frequency achievable by controller Can it be achieved? Depends on phase and gain margins 37
Central controller and size Control limitations Ideal open-loop L(s) Near crossover frequency, c, gain ~ ( a / s) k 38
Central controller and size Explicitly separate the non-minimum phase terms L( s) L ( s) L ( s) MP NMP Minimum phase component in vicinity of the crossover frequency is L ( s) ( a / s) MP Non-minimum phase component is Blaschke product L NMP 2 2 ( s 2 zs z ) ( s) 2 2 ( s 2 s ) z k z ; 0 1 39
Relation between ( c / z ) and PM is Denote positive solution by Relation for ( p / z ), where p is phase crossover frequency Denote positive solution by 2 2) / (1 ; 0 1 ) tan( 2 2 PM k c z c c z c ), ( PM k c 2 2) / (1 ; 0 1 ) tan( 2 2 k p z p p z p p (k) 40 Central controller and size
Central controller and size Relation between p, c, and GM is Hence p 20k log 10 GM c p c c p ( k) ( GM / 20k ) ( k, PM ) 10 Given PM and GM, solve for k ( k, PM ) c z c is the maximum possible crossover frequency 41
Central controller and size Apply to the 3MW and 5MW machines 3MW has tower frequency 2.6rad/s 5MW has tower frequency 2.0rad/s Rated wind speed are roughly 12m/s Greatest controller crossover frequency is required just above rated wind speed 42
Central controller and size With a GM of 10dB and a PM of 60deg 3MW, c =0.65rad/s at 12m/s c =1.04rad/s at 25m/s 5MW, c =0.27rad/s at 12m/s c =0.49rad/s at 25m/s With a GM of 6dB and a PM of 45deg 3MW, c =1.0rad/s at 12m/s 5MW, c =0.43rad/s at 12m/s 43
Central controller and size A bandwidth of 1rad/s is unachievable with a GM of 10dB and a PM of 60deg For the 3MW machine, a bandwidth of 1rad/s is achievable with a GM of 6dB and a PM of 45deg For the 5MW machine, a bandwidth of only 0.5rad/s is achievable Detailed design of controllers agreed with the above predictions 44
Central controller and size Tower and rotor induce RHPZs in the drive-train dynamics Attainable controller performance is restricted by these RHPZs The rotor induced RHPZs cause greater reduction in performance than the tower RHPZs Attainable controller performance degrades with increasing size of wind turbine Will this limit turbine size? 45
Central controller and size Tower + speed control Speed reference Tower+speed Pitch Turbine Tower acceleration controller Torque Dynamics Generator speed 46
Phase (deg) Magnitude (db) Central controller and size 50 Bode Diagram From: GSpRef To: Out(1) 0-50 -100-150 0-360 -720 PCC (Basic) - (16m/s) SISO (Basic) - (16m/s) -1080 10-2 10-1 10 0 10 1 10 2 Frequency (rad/sec) Non- minimum phase zeros removed dynamic 47
Central controller and size Above rated controller Tower Damper Speed reference - Speed Controller Torque reference + + Pitch Turbine Dynamics Tower acceleration Generator speed Drive-train Damper 48
Spectra (Nm 2 /rad) Cumulative spectra (Nm 2 ) Central controller and size x 10 14 Life-time equivalent load reductions 10% - 15% 10 15 10 10 SISO(Basic)_14m/s_Tower My [0] [Nm] SISO(Basic+TFL)_14m/s_Tower My [0] [Nm] PCC(Basic+TFL)_14m/s_Tower My [0] [Nm] 3 Improvement of tower feedback loop 50% - 100% 10 5 10 0 10 1 10 2 Frequency (rad/s) Tower base bending moments 49
Central controller and size Single Blade Control reference inputs central controller b d actuator + control actuator + control M 1 b 1 M 2 b 2 turbine dynamics rotor speed g actuator + control M 3 b 3 50
Load imbalance reduction Blade loads have a strong azimuth angle dependence Cause: Rotational sampling of the uneven wind-field Deterministic components tower shadow, wind sheer Stochastic components turbulence Concentrated at multiples of rotor speed W 0 51
Load imbalance reduction 1Ω o 2Ωo Edge frequency 3Ω o 52
Load imbalance reduction Applied Supergen Exemplar 2MW wind turbine Supergen Exemplar 5MW wind turbine Performance assessed for reduction Blade root bending moment Hub unbalanced load in rotating rotor frame Hub unbalanced loads in stationary frame Strong dependence of machine size 53
Load imbalance reduction The 2MW Supergen machine has following characteristics: Nominal Rotor Diameter: 75 m Tower height: 63.125 m Cut-in wind speed: 4 m/s Cut-out wind speed: 25 m/s Out-of-plane 1-st mode frequency: 6.65 rad/s In-plane 1-st mode frequency: 9.96 rad/s Tower 1-st Fore-aft mode: 2.54 rad/s Tower 1-st Side-side mode: 2.53 rad/s Nominal rotor speed is 1.867 rad/s. May 2009 54
--- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 2MW Supergen exemplar wind turbine x 10 6 x 10 14 2 1.5 Collective Pitch: Blade 1 My [1.25] [Nm] IA, Design 1: Blade 1 My [1.25] [Nm] IA, Design 2: Blade 1 My [1.25] [Nm] 1.9 1.8 1.7 1 1.6 0.5 1.5 0 Collective Pitch: Blade 1 My [1.25] [Nm] IA, Design 1: Blade 1 My [1.25] [Nm] IA, Design 2: Blade 1 My [1.25] [Nm] 55 60 65 70 75 80 85 Time (s) 1.3 10-1 10 0 10 1 Frequency (rad/s) Out-of-plane blade root bending moment 1.4 May 2009 55
--- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 2MW Supergen exemplar wind turbine x 10 6 x 10 13 1 0.5 0-0.5-1 Collective, Rotating hub My [Nm] IA, Des.1, Rotating hub My [Nm] IA, Des.2, Rotating hub My [Nm] -1.5 sim3_powprod10a_stationary hub My [Nm] sim2_powprod10a_stationary hub My [Nm] sim1_powprod_cc10a_stationary hub My [Nm] 55 60 65 70 75 80 85 Time (s) 10-1 10 0 10 1 0 Frequency (rad/s) Hub bending moment (nodding rotating coordinates) May 2009 56
--- [Nm] Load imbalance reduction x 10 6 2MW Supergen exemplar wind turbine 1.5 1 0.5 0-0.5-1 -1.5 Collective Control, Stationary hub My [Nm] IA, Design 1, Stationary hub My [Nm] IA, Design 2, Stationary hub My [Nm] 100 200 300 400 500 600 Time (s) Hub bending moment (nodding, stationary motion) May 2009 57
Load imbalance reduction 2MW Supergen exemplar wind turbine Blade 1 Mx Blade 1 My Blade 2 Mx Blade 2 My Blade 3 Mx Blade 3 My 1P D(%) 0.49 6.01 0.28 6.97 0.19 6.16 1P + 2P D(%) -2.88 7.24-3.74 7.99-5.32 7.56 Blade root bending moment reduction Rotating hub Mx Rotating hub My Rotating hub Mz Tower Mx Tower My 1P D(%) -0.19 8.45 8.38 1P D(%) 1.47 0.48 1P + 2P D(%) -1.45 10.02 9.71 1P + 2P D(%) 2.15-2.60 Hub moments (rotating) reduction Tower moments reduction May 2009 58
Load imbalance reduction The 5MW Supergen machine has following characteristics: Nominal Rotor Diameter: 126 m Tower height: 87.6 m Cut-in wind speed: 4 m/s Cut-out wind speed: 25 m/s Out-of-plane 1-st mode frequency: 4.57 rad/s In-plane 1-st mode frequency: 7.00 rad/s Tower 1-st Fore-aft mode: 1.75 rad/s Tower 1-st Side-side mode: 1.75 rad/s Nominal rotor speed is 1.237 rad/s. May 2009 59 59
--- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 5MW Supergen exemplar wind turbine x 10 6 x 10 14 10 8 6 4 2 0 5-2 -4-6 Collective Pitch: Blade 1 My [1.5] [Nm] 1P+2P IA: Blade 1 My [1.5] [Nm] 280 285 290 295 300 305 310 315 320 325 Time (s) Colelctive Pitch: Blade 1 My [1.5] [Nm] 1P IA: Blade 1 My [1.5] [Nm] 1P+2P IA: Blade 1 My [1.5] [Nm] 10 0 10 1 Frequency (rad/s) Out-of-plane blade root bending moment May 2009 60 60
--- [Nm] PSD (Nm 2 /rad) Cumulative PSD (Nm 2 ) Load imbalance reduction 5MW Supergen exemplar wind turbine 1 x 10 7 x 10 14 10 0.5 0-0.5 Collective Pitch: Rotating hub My [Nm] 1P IA: Rotating hub My [Nm] 1P+2P IA: Rotating hub My [Nm] 5-1 2-1.5 Collective Pitch: Rotating hub My [Nm] 1P+2P IA: Rotating hub My [Nm] 280 285 290 295 300 305 310 315 320 325 Time (s) 10 0 10 1 Frequency (rad/s) 0 Hub bending moment (nodding rotating coordinates) May 2009 61 61
--- [Nm] Load imbalance reduction 5MW Supergen exemplar wind turbine x 10 6 20 Collective, Stationary hub My [Nm] 1P IA, Stationary hub My [Nm] 1P+2P IA, Stationary hub My [Nm] 15 10 5 0-5 50 100 150 200 250 300 350 400 450 500 550 Time (s) May 2009 Hub bending moment (nodding, stationary motion) 62
Load imbalance reduction 5MW Supergen exemplar wind turbine 12000000 22% Blade lifetime fatigue reduction 10000000 8000000 6000000 Collective 1P+2P IA 1P+2P IA all 4000000 2000000 0 May 2009 4 4 4 6 6 6 8 8 8 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 63 63
9000000 Load imbalance reduction 5MW Supergen exemplar wind turbine 49.25% hub lifetime fatigue reduction (rotating) 8000000 7000000 6000000 5000000 4000000 3000000 Collective 1P+2P IA 1P+2P IA all 2000000 1000000 0 4 4 4 6 6 6 8 8 8 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 64
Load imbalance reduction 5MW Supergen exemplar wind turbine 6000000 24% hub lifetime fatigue reduction (stationary) 5000000 4000000 3000000 Collective 1P+2P IA 1P+2P IA all 2000000 1000000 0 4 4 4 6 6 6 8 8 8 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 May 2009 65 65
Load imbalance reduction 5MW Supergen exemplar wind turbine Blade 1 Mx Blade 1 My Blade 2 Mx Blade 2 My Blade 3 Mx Blade 3 My 1P D(%) 3.84 13.7 3.77 14.4 3.63 11.5 1P + 2P D(%) 1P + 2P all D(%) 3.61 15.8 3.65 17.1 3.47 14.3 4.32 22 4.43 24 3.76 21.9 Blade root bending moment reduction Rotating hub Mx Rotating hub My Rotating hub Mz Tower Mx Tower My 1P D(%) -0.41 23.94 24.28 1P D(%) -0.62-1.43 1P + 2P D(%) -0.76 27.78 28.07 1P + 2P D(%) 2.09 2.44 1P + 2P all D(%) -0.74 49.25 49.90 1P + 2P all D(%) 4.26 0.01 Hub moments (rotating) reduction May 2009 Tower moments reduction 66
Load imbalance reduction Load reductions greatly increased when change from 2MW to 5MW machine 50 40 30 20 10 0-10 5MW, 1P 2MW, D1 5MW, 1+2P, all 2MW, D1 2MW, D2 5MW, 1P 5MW, 1+2P 5MW, 1+2P, all May 2009 67 67
Conclusion Turbines are going to become even bigger Control will be a key enabling technology To enable operation of the turbines within design operating envelope To reduce load imbalances Next generation controllers will need to reduce loads even more 68
Thank you! Consortium 69